Aspire Faculty ID #15272 · Topic: JAMIA MCA 2016 · Just now
JAMIA MCA 2016

If $z$ be a complex number and $\bar{z}$ be its conjugate, then the number of solutions of $z^{2} + 2\bar{z} = 0$ is …

Solution

Let $z = x + iy$, then $\bar{z} = x - iy$. Substitute: $(x + iy)^{2} + 2(x - iy) = 0$. $\Rightarrow x^{2} - y^{2} + 2ixy + 2x - 2iy = 0$. Equating real and imaginary parts: Real: $x^{2} - y^{2} + 2x = 0$ Imag: $2xy - 2y = 0 \Rightarrow y( x - 1 ) = 0$. If $y=0$, then $x^{2} + 2x = 0 \Rightarrow x = 0, -2$. If $x=1$, then $1 - y^{2} + 2 = 0 \Rightarrow y^{2} = 3$. Hence, total 4 solutions.
← Previous Next →

Previous 10 Questions — JAMIA MCA 2016

Nearest first
1
The amplitude of $\dfrac{1+i\sqrt{3}}{\sqrt{3}+i}$ is equal to …
Topic: JAMIA MCA 2016
 2
If $\cos^{2}\theta + \sec^{2}\theta = a$, then …
Topic: JAMIA MCA 2016
 3
If $\cos\theta + \cos^{3}\theta = \sin^{2}\theta$, then $\sin^{6}\theta - 4\sin^{4}\theta + 8\sin^{2}\theta$ is equal t…
Topic: JAMIA MCA 2016
 4
The value of $\tan1^{\circ} \cdot \tan2^{\circ} \cdot \tan3^{\circ} \cdots \tan89^{\circ}$ is …
Topic: JAMIA MCA 2016
 5
If $\cos\theta + \sec\theta = 3$, then $\cos^{2}\theta + \sec^{2}\theta$ is …
Topic: JAMIA MCA 2016
 6
The value of $2\sin^{2}\theta \cdot \cos^{2}\theta (\sec^{2}\theta + \csc^{2}\theta)$ is …
Topic: JAMIA MCA 2016
 7
$\displaystyle \int \sqrt{x}e^{\sqrt{x}}dx$ is equal to …
Topic: JAMIA MCA 2016
 8
$\displaystyle \int_{0}^{1}\frac{x}{(1-x)^{1/2}}dx$ is equal to …
Topic: JAMIA MCA 2016
 9
$\displaystyle \int_{0}^{\frac{\pi}{4}}\sec^{2}x\sin x\,dx=a+\sqrt{2}$, find $a$
Topic: JAMIA MCA 2016
 10
If $x>0$, then $\displaystyle \int |x|^{3} dx$ is equal to …
Topic: JAMIA MCA 2016

Next 10 Questions — JAMIA MCA 2016

Ascending by ID
1
If $z$ be a complex number, then one of the solutions of the equation $z^{2} + |z|^{2} = 0$ is …
Topic: JAMIA MCA 2016
 2
If $\omega$ is a cube root of unity, then the value of $(1 + \omega - \omega^{2})(1 - \omega + \omega^{2})$ is …
Topic: JAMIA MCA 2016
 3
Let cube roots of unity be $1, \omega, \omega^{2}$. Which of the following is a cube root of the equation $(x - 1)^{3} …
Topic: JAMIA MCA 2016
 4
If $m^{\text{th}}$ term of an A.P. is $n$ and $n^{\text{th}}$ term is $m$, then its $10^{\text{th}}$ term is …
Topic: JAMIA MCA 2016
 5
Let sum of $n$ terms of an A.P. be $S_n=3n^2+5$. If $T_n$ (the $n$th term) of this series is $159$, then $n$ is …
Topic: JAMIA MCA 2016
 6
If the roots of $x^3-9x^2+23x-15=0$ are in A.P., then their common difference is …
Topic: JAMIA MCA 2016
 7
If $\log_{2}(5\cdot2^{x}+1),\ \log_{4}(2^{\,1-x}+1)$ and $1$ are in A.P., then $x$ equals …
Topic: JAMIA MCA 2016
 8
If sum of $n$ terms of a series is $3n^2 + 4n$, then the series is …
Topic: JAMIA MCA 2016
 9
If ${}^8C_r - {}^7C_3 = {}^7C_2$, then $r$ is equal to …
Topic: JAMIA MCA 2016
 10
The number of arrangements of the letters of the word BANANA in which two N’s do not appear adjacently is …
Topic: JAMIA MCA 2016
Ask Your Question or Put Your Review.

loading...